Problem: Which decimal is equivalent to $\dfrac{25}{6}$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $4.\overline{1}$ (Choice B) B $4.\overline{16}$ (Choice C) C $4.1\overline{6}$ (Choice D) D $4.1\overline{667}$
Solution: $ \dfrac{25}{6}$ represents $25 \div 6$. ${6}$ ${2}$ ${5}$ ${0}$ $\text{How many times does }6\text{ go into }{25}\text{?}$ ${4}$ ${2}$ ${4}$ $-$ ${1}$ ${25}\div6={4}\text{ with a remainder of }{1}$ ${0}$ ${.}$ ${.}$ $\text{Write in a decimal and a zero.}$ $\text{How many times does }6\text{ go into }{10}\text{?}$ ${0}$ ${0}$ ${1}$ ${6}$ $-$ ${4}$ ${10}\div6={1}\text{ with a remainder of }{4}$ $\text{How many times does }6\text{ go into }{40}\text{?}$ ${0}$ ${0}$ ${6}$ ${3}$ ${6}$ $-$ ${4}$ ${40}\div6={6}\text{ with a remainder of }{4}$ $\text{How many times does }6\text{ go into }{40}\text{?}$ ${0}$ ${0}$ ${6}$ ${3}$ ${6}$ $-$ ${4}$ ${40}\div6={6}\text{ with a remainder of }{4}$ $\text{How many times does }6\text{ go into }{40}\text{?}$ ${0}$ ${0}$ ${6}$ ${6}$ ${3}$ ${6}$ $-$ ${4}$ ${4}$ ${40}\div6={6}\text{ with a remainder of }{4}$ Notice how the decimal is repeating and will continue to repeat as we bring down more zeros. So $\dfrac{25}{6}$ is equivalent to $4.1\overline{6}$.